Mixup

The problem, from first principles

Neural networks tend to memorize training images and become overconfident between them. Mixup is an augmentation that teaches them to behave linearly between examples: build a new training example as a weighted average of two images, and give it the same weighted average of their (one-hot) labels. A picture that is 70% cat and 30% dog gets the label "0.7 cat, 0.3 dog". The mixing weight lam is drawn from a Beta distribution with parameter alpha. Small alpha means lam is usually near 0 or 1 (a mild mix), and alpha = 1 makes it uniform on [0, 1].

From theory to code

Implement sample_lambda and mixup.

Constraints

• sample_lambda(alpha, rng) returns rng.beta(alpha, alpha) with exactly one call to rng.beta, where rng is a np.random.RandomState.
• mixup(x1, y1, x2, y2, lam) returns (lam * x1 + (1 - lam) * x2, lam * y1 + (1 - lam) * y2). Images and one-hot label vectors are NumPy arrays of matching shapes.
• lam is a float in [0, 1]. Do not modify the inputs.

Hints